Question

A 160cm long string has two adjacent resonance at 85hz frequencies . calculate : 1- the fundamental frequency , 2- the speed of the wave
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Answer 1

Length=l=160cm=1.6m

Frequency=85Hz

#1

Fundamental frequency be v

$\\ \sf\bull\longmapsto v=\dfrac{\nu}{2\ell}$

$\\ \sf\bull\longmapsto v=\dfrac{85}{2(1.6)}$

$\\ \sf\bull\longmapsto v=\dfrac{85}{3.2}$

$\\ \sf\bull\longmapsto v=26.6Hz$

#2

First we have to find wavelength

$\\ \sf\bull\longmapsto \lambda=\dfrac{c}{v}$

$\\ \sf\bull\longmapsto \lambda=\dfrac{3\times 10^8ms^{-1}}{26.6}$

$\\ \sf\bull\longmapsto \lambda=0.112\times 10^8m$

$\\ \sf\bull\longmapsto \lambda=112\times 10^5m$

$\\ \sf\bull\longmapsto \lambda=1.12\times 10^6m$

Now..

Velocity be v

$\\ \sf\bull\longmapsto v=f\lambda$

• f is frequency

$\\ \sf\bull\longmapsto v=26.5\times1.12\times 10^6m$

$\\ \sf\bull\longmapsto v=29.68\times 10^6$

$\\ \sf\bull\longmapsto v=2.9\times 10^7m/s$